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A vector whose direction is unchanged by a given transformation and whose magnitude is changed by a factor corresponding to that vector's eigenvalue. In quantum mechanics, the transformations involved are operators corresponding to a physical system's observables. The eigenvectors correspond to possible states of the system, and the eigenvalues to possible observed values.

[Partial translation of German Eigenvektor : eigen-, characteristic; see eigenvalue + Vektor, vector.]


(Mathematics) maths physics a vector x satisfying an equation Ax = λx, where A is a square matrix and λ is a constant
References in periodicals archive ?
In the second section, we describe the method of finding the fixed point and the associated eigenvectors in the perturbed system and show a three-dimensional manifold structure is obtained from the Poincare map.
d) Repeat this process until the eigenvector solution does not change from the previous iteration.
The eigenvector engine searches widely first and gathers many sites [the "root" set].
Eigenvector centrality is obtained based on the connectivity of neighbouring nodes.
The authors use the idea of an alternative approach that carries over spectral information from one linear system to the next by extracting approximations of eigenvectors and using them in a deflation framework [2,29, 30,41].
Most of these approaches is based on calculation of eigenvectors and eigenvalues [11] of data matrix D.
In further research it is necessary to practically confirm suggested algorithm, compare it with previous algorithm and use symmetry properties of eigenvector.
This is the objective function of LDA, the solution w is now the largest eigenvector of [S.
Each eigenvector of our generalized eigenproblem (20) corresponds to an eigenvector of matrix M.
The eigenvector corresponding to the larger eigenvalue [lambda]1 gives the main orientation of the cloud of points, namely the direction of its first axis of inertia.